Computationally efficient variational-like approximations of possibilistic inferential models

Abstract

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple yet powerful numerical strategy for approximating the IM's possibility contour, or at least its $\alpha$-cut for a specified $\alpha \in (0,1)$. Our proposal starts with the specification of a parametric family that, in a certain sense, approximately covers the credal set associated with the IM's possibility measure. Akin to variational inference, we then propose to tune the parameters of that parametric family so that its $100(1-\alpha)\%$ credible set roughly matches the IM contour's $\alpha$-cut. This parametric $\alpha$-cut matching strategy implies a full approximation to the IM's possibility contour at a fraction of the computational cost associated with previous strategies.